7 problems

Toral-component surjectivity conjecture. For all sufficiently large $i$, $\Pi_{i}$ is surjective onto ${\mathcal V}$.

Boundary-image conjecture. For any component ${\mathcal E}_{0}$ of ${\mathcal E}$, $\bar{\Pi}(\partial {\mathcal E}_{0})$ has empty interior in ${\mathcal C}$.

Let $M$ be a manifold with boundary, let ${\mathcal E}={\mathcal E}(M)$ denote the moduli space of Poincaré–Einstein metrics on $M$, and let $\mathfrak c$ assign to each conformall…

Fefferman–Graham flatness conjecture. There exists a metric representative in $(M_+,\boldsymbol{c})$ that is formally to all orders Poincaré–Einstein.

Anderson's cusp-formation conjecture. Cusp formation is not possible on the $4$-ball.

Let $N\geq1$ satisfy $2N\leq n$ when $n$ is even. On any Riemannian manifold $(M,g)$ of dimension $n\geq3$, let $D_{2},D_{4},\ldots$ be the symmetric bilinear forms defined by … wh…

Let $n$ be even and $2N\leq n$, or let $n$ be odd with arbitrary $N$. Define $\Lambda_{2j}=Q_{2j}-{\mathcal Q}_{2j}$, where $Q_{2j}$ is the Q-curvature and ${\mathcal Q}_{2j}$ its…